 14.141: An article in Industrial Quality Control (1956, pp. 58) describes a...
 14.142: An engineer suspects that the surface finish of metal parts is infl...
 14.143: In the book Design and Analysis of Experiments, 7th edition (2009, ...
 14.144: An experiment was conducted to determine whether either firing temp...
 14.145: An article in Technometrics [Exact Analysis of Means with Unequal V...
 14.146: Johnson and Leone (Statistics and Experimental Design in Engineerin...
 14.147: An article in the IEEE Transactions on Electron Devices (November 1...
 14.148: An article in the Journal of Testing and Evaluation (1988, Vol. 16,...
 14.149: Consider a twofactor factorial experiment. Develop a formula for f...
 14.1410: The quality control department of a fabric finishing plant is study...
 14.1411: The percentage of hardwood concentration in raw pulp, the freeness,...
 14.1412: An engineer is interested in the effect of cutting speed (A), metal...
 14.1413: Four factors are thought to influence the taste of a softdrink bev...
 14.1414: The data shown here represent a single replicate of a 25 design tha...
 14.1415: An article in IEEE Transactions on Semiconductor Manufacturing (Vo...
 14.1416: An article in Oikos: A Journal of Ecology [Regulation of Root Vole ...
 14.1417: An experiment was run in a semiconductor fabrication plant in an ef...
 14.1418: An experiment described by M. G. Natrella in the National Bureau of...
 14.1419: Consider the data from Exercise 1412. Suppose that the data from t...
 14.1420: A 24 factorial design was run in a chemical process. The design fac...
 14.1421: An experiment has run a single replicate of a 24 design and calcula...
 14.1422: A twolevel factorial experiment in four factors was conducted by C...
 14.1423: Consider a factorial experiment with four center points. The data a...
 14.1424: Consider the experiment in Exercise 1414. Suppose that a center po...
 14.1425: Consider the experiment in Exercise 1417. Suppose that a center po...
 14.1426: An article in Talanta (2005, Vol. 65, pp. 895899) presented a 23 fa...
 14.1427: An experiment to study the effect of machining factors on ceramic s...
 14.1428: Consider the following Minitab output for a 23 factorial experiment...
 14.1429: An article in Analytica Chimica Acta [DesignofExperiment Optimizat...
 14.1430: Consider the data from the first replicate of Exercise 1412. (a) S...
 14.1431: Consider the data from the first replicate of Exercise 1413. (a) C...
 14.1432: Consider the data from Exercise 1418. (a) Construct the design tha...
 14.1433: Construct a 25 design in two blocks. Select the ABCDE interaction t...
 14.1434: Consider the data from the first replicate of Exercise 1413, assum...
 14.1435: Construct a 25 design in four blocks. Select the appropriate effect...
 14.1436: Consider the 26 factorial design. Set up a design to be run in four...
 14.1437: An article in Quality Engineering [Designed Experiment to Stabilize...
 14.1438: An article in Industrial and Engineering Chemistry [Factorial Exper...
 14.1439: Consider the following Minitab output from a single replicate of a ...
 14.1440: An article in Advanced Semiconductor Manufacturing Conference (ASMC...
 14.1441: Consider the problem in Exercise 1417. Suppose that only half of t...
 14.1442: Suppose that in Exercise 1420 it was possible to run only a 1 2 fr...
 14.1443: An article by L. B. Hare [In the Soup: A Case Study to Identify Con...
 14.1444: Montgomery (2009) described a 241 fractional factorial design used ...
 14.1445: R. D. Snee (Experimenting with a Large Number of Variables, in Expe...
 14.1446: An article in Quality Engineering [A Comparison of Multiresponse O...
 14.1447: An article in Industrial and Engineering Chemistry [More on Plannin...
 14.1448: Suppose that in Exercise 1414 only a 1 4 fraction of the 25 design...
 14.1449: For each of the following designs write down the aliases, assuming ...
 14.1450: Consider the 262 design in Table 1429. (a) Suppose that after anal...
 14.1451: An article in the Journal of Radioanalytical and Nuclear Chemistry ...
 14.1452: An article in the Journal of Marketing Research (1973, Vol. 10, No....
 14.1453: An article in Rubber Age (Vol. 89, 1961, pp. 453 458) describes an ...
 14.1454: An article in Quality Engineering [Mean and Variance Modeling with ...
 14.1455: Consider the firstorder model where 1 xi 1. Find the direction of ...
 14.1456: A manufacturer of cutting tools has developed two empirical equatio...
 14.1457: An article in Tappi (1960, Vol. 43, pp. 3844) describes an experime...
 14.1458: In their book Empirical Model Building and Response Surfaces (John ...
 14.1459: Consider the firstorder model where . (a) Find the direction of st...
 14.1460: An article in the Journal of Materials Processing Technology (1997,...
 14.1461: An article in Process Engineering (1992, No. 71, pp. 4647) presents...
 14.1462: Heat treating of metal parts is a widely used manufacturing process...
 14.1463: An article in the Textile Research Institute Journal (1984, Vol. 54...
 14.1464: An article in the IEEE Transactions on Components, Hybrids, and Man...
 14.1465: An article in Solid State Technology (Vol. 29, 1984, pp. 281284) de...
 14.1466: An article in the Journal of Coatings Technology (Vol. 60, 1988, pp...
 14.1467: An article in the Journal of Manufacturing Systems (Vol. 10, 1991, ...
 14.1468: Construct a design for the problem in Exercise 1466. Select the da...
 14.1469: Construct a design for the problem in Exercise 1467. Select the da...
 14.1470: Construct a design in 16 runs. What are the alias relationships in ...
 14.1471: Construct a design in eight runs. What are the alias relationships ...
 14.1472: An article in the Journal of Quality Technology (Vol. 17, 1985, pp....
 14.1473: An article in the Journal of Quality Technology (Vol. 17, 1985, pp....
 14.1474: An article in Tropical Science [Proximate Composition of the Seeds ...
 14.1475: An article in Plant Disease [Effect of Nitrogen and Potassium Ferti...
 14.1476: An article in Biotechnology Progress (2001, Vol. 17, pp. 366368) re...
 14.1477: An article in the Journal of Applied Electrochemistry (May 2008, Vo...
 14.1478: An article in Biotechnology Progress (December (a) Write down the c...
 14.1479: The rework time required for a machine was found to depend on the s...
 14.1480: Consider the following results from a twofactor experiment with tw...
 14.1481: Consider the following ANOVA table from a twofactor factorial exper...
 14.1482: An article in Process Biochemistry (Dec. 1996, Vol. 31, No. 8, pp. ...
 14.1483: Consider an unreplicated 2k factorial, and suppose that one of the ...
 14.1484: What blocking scheme would you recommend if it were necessary to ru...
 14.1485: Consider a 22 design in two blocks with AB confounded with blocks. ...
 14.1486: Consider a 23 design. Suppose that the largest number of runs that ...
 14.1487: Construct a 251 design. Suppose that it is necessary to run this de...
 14.1488: Construct a design. Show how this design may be confounded in four ...
 14.1489: Construct a design. Show how this design can be confounded in two b...
 14.1490: Set up a design using D AB, E AC, F BC, and G ABC as the design gen...
 14.1491: Consider the square root of the sum of squares for curvature and di...
Solutions for Chapter 14: Design of Experiments with Several Factors
Full solutions for Applied Statistics and Probability for Engineers  5th Edition
ISBN: 9780470053041
Solutions for Chapter 14: Design of Experiments with Several Factors
Get Full SolutionsThis textbook survival guide was created for the textbook: Applied Statistics and Probability for Engineers, edition: 5. This expansive textbook survival guide covers the following chapters and their solutions. Applied Statistics and Probability for Engineers was written by and is associated to the ISBN: 9780470053041. Chapter 14: Design of Experiments with Several Factors includes 91 full stepbystep solutions. Since 91 problems in chapter 14: Design of Experiments with Several Factors have been answered, more than 22704 students have viewed full stepbystep solutions from this chapter.

aerror (or arisk)
In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error).

Analytic study
A study in which a sample from a population is used to make inference to a future population. Stability needs to be assumed. See Enumerative study

Attribute
A qualitative characteristic of an item or unit, usually arising in quality control. For example, classifying production units as defective or nondefective results in attributes data.

Average
See Arithmetic mean.

Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.

Bernoulli trials
Sequences of independent trials with only two outcomes, generally called “success” and “failure,” in which the probability of success remains constant.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

Central tendency
The tendency of data to cluster around some value. Central tendency is usually expressed by a measure of location such as the mean, median, or mode.

Chisquare (or chisquared) random variable
A continuous random variable that results from the sum of squares of independent standard normal random variables. It is a special case of a gamma random variable.

Conditional mean
The mean of the conditional probability distribution of a random variable.

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

Covariance matrix
A square matrix that contains the variances and covariances among a set of random variables, say, X1 , X X 2 k , , … . The main diagonal elements of the matrix are the variances of the random variables and the offdiagonal elements are the covariances between Xi and Xj . Also called the variancecovariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix.

Cumulative distribution function
For a random variable X, the function of X deined as PX x ( ) ? that is used to specify the probability distribution.

Designed experiment
An experiment in which the tests are planned in advance and the plans usually incorporate statistical models. See Experiment

Error mean square
The error sum of squares divided by its number of degrees of freedom.

Error of estimation
The difference between an estimated value and the true value.

Error variance
The variance of an error term or component in a model.

Ftest
Any test of signiicance involving the F distribution. The most common Ftests are (1) testing hypotheses about the variances or standard deviations of two independent normal distributions, (2) testing hypotheses about treatment means or variance components in the analysis of variance, and (3) testing signiicance of regression or tests on subsets of parameters in a regression model.

Gamma random variable
A random variable that generalizes an Erlang random variable to noninteger values of the parameter r

Gaussian distribution
Another name for the normal distribution, based on the strong connection of Karl F. Gauss to the normal distribution; often used in physics and electrical engineering applications